Which of the following numbers is a multiple of 8? ${42,61,64,68,84}$
The multiples of $8$ are $8$ $16$ $24$ $32$ ..... In general, any number that leaves no remainder when divided by $8$ is considered a multiple of $8$ We can start by dividing each of our answer choices by $8$ $42 \div 8 = 5\text{ R }2$ $61 \div 8 = 7\text{ R }5$ $64 \div 8 = 8$ $68 \div 8 = 8\text{ R }4$ $84 \div 8 = 10\text{ R }4$ The only answer choice that leaves no remainder after the division is $64$ $ 8$ $8$ $64$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $8$ are contained within the prime factors of $64$ $64 = 2\times2\times2\times2\times2\times2 8 = 2\times2\times2$ Therefore the only multiple of $8$ out of our choices is $64$. We can say that $64$ is divisible by $8$.